mlsanityData to 7 Oct 2026

Decision-Dependent Stochastic Optimization: The Role of Distribution Dynamics

arXiv 2503.07324 ↗First posted 10 Mar 2025math.OC cs.LG cs.SYcited by 5

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Abstract (arXiv)

Distribution shifts have long been regarded as troublesome external forces that a decision-maker should either counteract or conform to. An intriguing feedback phenomenon termed decision dependence arises when the deployed decision affects the environment and alters the data-generating distribution. In the realm of performative prediction, this is encoded by distribution maps parameterized by decisions due to strategic behaviors. In contrast, we formalize an endogenous distribution shift as a feedback process featuring nonlinear dynamics that couple the evolving distribution with the decision. Stochastic optimization in this dynamic regime provides a fertile ground to examine the various roles played by dynamics in the composite problem structure. To this end, we develop an online algorithm that achieves optimal decision-making by both adapting to and shaping the dynamic distribution. Throughout the paper, we adopt a distributional perspective and demonstrate how this view facilitates characterizations of distribution dynamics and the optimality and generalization performance of the proposed algorithm. We showcase the theoretical results in an opinion dynamics context, where an opportunistic party maximizes the affinity of a dynamic polarized population, and in a recommender system scenario, featuring performance optimization with discrete distributions in the probability simplex.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 44 of its 59 references that are in the map. First posted on arXiv 10 Mar 2025.

Builds on

44 of 59 references.

References · 44

  1. 2016Optimization Methods for Large-Scale Machine Learningcited by 1,140
  2. 2013Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programmingcited by 716
  3. 2018Learning Models with Uniform Performance via Distributionally Robust Optimizationcited by 334
  4. 2020Performative Predictioncited by 318
  5. 2021Outside the Echo Chamber: Optimizing the Performative Riskcited by 95
  6. 2018Tight Analyses for Non-Smooth Stochastic Gradient Descentcited by 94
  7. 2020Stochastic Optimization for Performative Predictioncited by 92
  8. 2020Performative Prediction in a Stateful Worldcited by 90
  9. 2021How to Learn when Data Reacts to Your Model: Performative Gradient Descentcited by 70
  10. 2020Stochastic optimization with decision-dependent distributionscited by 65
  11. 2021Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learningcited by 65
  12. 2020A High Probability Analysis of Adaptive SGD with Momentumcited by 61
32 more
  1. 2022Learning in Mean Field Games: A Surveycited by 56
  2. 2023Performative Prediction: Past and Futurecited by 52
  3. 2021Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overviewcited by 42
  4. 2022Multiplayer Performative Prediction: Learning in Decision-Dependent Gamescited by 42
  5. 2022Regret Minimization with Performative Feedbackcited by 40
  6. 2021State Dependent Performative Prediction with Stochastic Approximationcited by 38
  7. 2022Multi-agent Performative Prediction: From Global Stability and Optimality to Chaoscited by 33
  8. 2020High Probability Convergence Bounds for Non-convex Stochastic Gradient Descent with Sub-Weibull Noisecited by 31
  9. 2020Time-Varying Convex Optimization: Time-Structured Algorithms and Applicationscited by 31
  10. 2022Decision-Dependent Risk Minimization in Geometrically Decaying Dynamic Environmentscited by 31
  11. 2020Online Stochastic Optimization with Wasserstein Based Non-stationaritycited by 25
  12. 2022Preference Dynamics Under Personalized Recommendationscited by 25
  13. 2022Performative Reinforcement Learningcited by 25
  14. 2022Multi-agent Performative Prediction with Greedy Deployment and Consensus Seeking Agentscited by 23
  15. 2021Online Projected Gradient Descent for Stochastic Optimization with Decision-Dependent Distributionscited by 17
  16. 2021Polarization in Geometric Opinion Dynamicscited by 16
  17. 2017A Tutorial on Modeling and Analysis of Dynamic Social Networks. Part Icited by 15
  18. 2020A New One-Point Residual-Feedback Oracle For Black-Box Learning and Controlcited by 14
  19. 2021Stochastic Optimization under Distributional Driftcited by 13
  20. 2024Accounting for AI and Users Shaping One Another: The Role of Mathematical Modelscited by 11
  21. 2023Zero-Regret Performative Prediction Under Inequality Constraintscited by 10
  22. 2024Model-Based RL for Mean-Field Games is not Statistically Harder than Single-Agent RLcited by 9
  23. 2019A Geometric Model of Opinion Polarizationcited by 7
  24. 2021Optimization Algorithms as Robust Feedback Controllerscited by 7
  25. 2022Stochastic Saddle Point Problems with Decision-Dependent Distributionscited by 6
  26. 2024Performative Control for Linear Dynamical Systemscited by 6
  27. 2018Distributionally Robust Optimization with Decision Dependent Ambiguity Setscited by 5
  28. 2023Dynamic Programming in Probability Spaces via Optimal Transportcited by 5
  29. 2023Strategic Distribution Shift of Interacting Agents via Coupled Gradient Flowscited by 5
  30. 2019Distributionally Robust Facility Location Problem under Decision-dependent Stochastic Demandcited by 4
  31. 2022Distributional Uncertainty Propagation via Optimal Transportcited by 4
  32. 2023The Impact of Recommendation Systems on Opinion Dynamics: Microscopic versus Macroscopic Effectscited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 3.

5 papers.

  1. 2025Performative Policy Gradient: Optimality in Performative Reinforcement Learningcited by 4
  2. 2025A Systems-Theoretic View on the Convergence of Algorithms under Disturbancescited by 0
  3. 2026When Predictions Shape Reality: A Socio-Technical Synthesis of Performative Predictions in Machine Learningcited by 0
  4. 2026Robust Strategic Classification under Decision-Dependent Cost Uncertaintycited by 0
  5. 2026Foundations of Reinforcement Learning and Control:Connections and New Perspectivescited by 0